The journalist who interviewed her about her alleged rape, but did not report the story, was also found guilty by a judge in the capital, Mogadishu.
Judge Ahmed Aden Farah said the woman would not go to jail immediately as she is caring for a young child.
A BBC reporter in Mogadishu says there has been an angry reaction to the case.
Many human rights groups and journalists say it is politically motivated, the BBC's Mohamed Mwalimu reports from Mogadishu.
Judge Farah said the court based its decision on medical evidence that the woman was not raped.
The woman had reported the alleged rape at a police station in Hodan, a district in Mogadishu where many displaced people live.
"We sentence her for offending state institutions by claiming she was raped," the AFP news agency quotes the judge as saying.
"She will spend one year in prison after finishing the breast feeding of her baby."